Fremlin, DH and Mendoza, J (1994) On the integration of vector-valued functions. Illinois Journal of Mathematics, 38 (1). pp. 127-147. DOI https://doi.org/10.1215/ijm/1255986891
Fremlin, DH and Mendoza, J (1994) On the integration of vector-valued functions. Illinois Journal of Mathematics, 38 (1). pp. 127-147. DOI https://doi.org/10.1215/ijm/1255986891
Fremlin, DH and Mendoza, J (1994) On the integration of vector-valued functions. Illinois Journal of Mathematics, 38 (1). pp. 127-147. DOI https://doi.org/10.1215/ijm/1255986891
Abstract
We discuss relationships between the McShane, Pettis, Talagrand and Bochner integrals. A large number of different methods of integration of Banach-space-valued functions have been introduced, based on the various possible constructions of the Lebesgue integral. They commonly run fairly closely together when the range space is separable (or has w^*-separable dual) and diverge more or less sharply for general range spaces. The McShane integral as described by [Go] is derived from the `gauge-limit' integral of [McS]. Here we give both positive and negative results concerning it and the other three integrals listed above.
Item Type: | Article |
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Uncontrolled Keywords: | math.FA |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 22 Apr 2021 14:59 |
Last Modified: | 07 Aug 2024 18:43 |
URI: | http://repository.essex.ac.uk/id/eprint/21545 |
Available files
Filename: 1255986891.pdf